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4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
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15 include "static_2/notation/relations/stareqsn_6.ma".
16 include "static_2/syntax/genv.ma".
17 include "static_2/static/reqx.ma".
19 (* SORT-IRRELEVANT EQUIVALENCE FOR CLOSURES ON REFERRED ENTRIES *************)
21 inductive feqx (G) (L1) (T1): relation3 genv lenv term ≝
22 | feqx_intro_sn: ∀L2,T2. L1 ≛[T1] L2 → T1 ≛ T2 →
27 "sort-irrelevant equivalence on referred entries (closure)"
28 'StarEqSn G1 L1 T1 G2 L2 T2 = (feqx G1 L1 T1 G2 L2 T2).
30 (* Basic_properties *********************************************************)
32 lemma feqx_intro_dx (G):
33 ∀L1,L2,T2. L1 ≛[T2] L2 →
34 ∀T1. T1 ≛ T2 → ❪G,L1,T1❫ ≛ ❪G,L2,T2❫.
35 /3 width=3 by feqx_intro_sn, teqx_reqx_div/ qed.
37 (* Basic inversion lemmas ***************************************************)
39 lemma feqx_inv_gen_sn:
40 ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ →
41 ∧∧ G1 = G2 & L1 ≛[T1] L2 & T1 ≛ T2.
42 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2 /2 width=1 by and3_intro/
45 lemma feqx_inv_gen_dx:
46 ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ →
47 ∧∧ G1 = G2 & L1 ≛[T2] L2 & T1 ≛ T2.
48 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
49 /3 width=3 by teqx_reqx_conf_sn, and3_intro/
52 (* Basic_2A1: removed theorems 6:
53 fleq_refl fleq_sym fleq_inv_gen
54 fleq_trans fleq_canc_sn fleq_canc_dx